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12 August, 18:29

A train moving with a velocity of 87.1 km/hour North, increases its speed with a uniform acceleration of 0.250 m/s2 North until it reaches a velocity of 160.0 km/hour North. What distance did the train travel while it was increasing its velocity, in units of meters?

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  1. 12 August, 21:32
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    2780 meters

    Explanation:

    First, convert km/hr to m/s.

    87.1 km/hr * (1000 m / km) * (1 hr / 3600 s) = 24.2 m/s

    160.0 km/hr * (1000 m / km) * (1 hr / 3600 s) = 44.4 m/s

    Given:

    v₀ = 24.2 m/s

    v = 44.4 m/s

    a = 0.250 m/s²

    Find: x

    v² = v₀² + 2a (x - x₀)

    (44.4 m/s) ² = (24.2 m/s) ² + 2 (0.250 m/s²) (x - 0 m)

    x = 2780 m
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